Reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algo...
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Reduced-order identification algorithms are usually used in machine learning and big data technologies, where the large-scale systems widely exist. For large-scale system identification, traditional least squares algorithm involves high-order matrix inverse calculation, while traditional gradient descent algorithm has slow convergence rates. The reduced-order algorithm proposed in this paper has some advantages over the previous work: (1) via sequential partitioning of the parameter vector, the calculation of the inverse of a high-order matrix can be reduced to low-order matrix inverse calculations;(2) has a better conditioned information matrix than that of the gradient descent algorithm, thus has faster convergence rates;(3) its convergence rates can be increased by using the Aitken acceleration method, therefore the reduced-order based Aitken algorithm is at least quadratic convergent and has no limitation on the step-size. The properties of the reduced-order algorithm are also given. Simulation results demonstrate the effectiveness of the proposed algorithm. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Discrete Markov random fields form a natural class of models to represent images and spatial datasets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes par...
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Discrete Markov random fields form a natural class of models to represent images and spatial datasets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and a fully Bayesian treatment of discrete Markov random fields difficult. We apply approximation theory for pseudo-Boolean functions to binary Markov random fields and construct approximations and upper and lower bounds for the associated computationally intractable normalising constant. As a by-product of this process we also get a partially ordered Markov model approximation of the binary Markov random field. We present numerical examples with both the pairwise interaction Ising model and with higher-order interaction models, showing the quality of our approximations and bounds. We also present simulation examples and one real data example demonstrating how the approximations and bounds can be applied for parameter estimation and to handle a fully Bayesian model computationally.
The present paper introduces a new kind of representation for the potentials in a Bayesian network: binary probability trees. They enable the representation of context-specific independences in more detail than probab...
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The present paper introduces a new kind of representation for the potentials in a Bayesian network: binary probability trees. They enable the representation of context-specific independences in more detail than probability trees. This enhanced capability leads to more efficient inference algorithms for some types of Bayesian networks. This paper explains the procedure for building a binary probability tree from a given potential, which is similar to the one employed for building standard probability trees. It also offers a way of pruning a binary tree in order to reduce its size. This allows us to obtain exact or approximate results in inference depending on an input threshold. This paper also provides detailed algorithms for performing the basic operations on potentials (restriction, combination and marginalization) directly to binary trees. Finally, some experiments are described where binary trees are used with the variable elimination algorithm to compare the performance with that obtained for standard probability trees. (C) 2010 Elsevier Inc. All rights reserved.
Aiming at the complexity of the mission planning result assessment index, the subjective factors of the assessment system and the unreasonable assessment method, an assessment method of mission planning quality based ...
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ISBN:
(纸本)9781538676042
Aiming at the complexity of the mission planning result assessment index, the subjective factors of the assessment system and the unreasonable assessment method, an assessment method of mission planning quality based on static Bayesian network is proposed. In this paper, the mathematical model of mission planning assessment is established. According to the expert knowledge, each impact factor and its conditional probability table are established. The variable elimination algorithm is used to make objective and quantitative reasoning of the mission planning result. From the simulation results, the static Bayesian method has high applicability and accuracy for the assessment of mission planning results with diverse indicators, different dimensions and vague values.
The present paper introduces a new kind of representation for the potentials in a Bayesian network: Binary Probability Trees. They allow to represent finer grain context-specific independences than those which can be ...
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ISBN:
(纸本)9783642029059
The present paper introduces a new kind of representation for the potentials in a Bayesian network: Binary Probability Trees. They allow to represent finer grain context-specific independences than those which can be encoded with probability trees. This enhanced capability leads to more efficient inference algorithms in some types of Bayesian networks. The paper explains how to build a binary tree from a given potential with a similar procedure to the one employed for probability trees. It also offers a way of pruning a binary tree if exact inference cannot be performed with exact trees, and provides detailed algorithms for performing directly with binary trees the basic operations on potentials (restriction, combination and marginalization). Finally, some experiments are shown that use binary trees with the variable elimination algorithm to compare the performance with standard probability trees.
The present paper introduces a new kind of representation for the potentials in a Bayesian network: binary probability trees. They enable the representation of context-specific independences in more detail than probab...
详细信息
The present paper introduces a new kind of representation for the potentials in a Bayesian network: binary probability trees. They enable the representation of context-specific independences in more detail than probability trees. This enhanced capability leads to more efficient inference algorithms for some types of Bayesian networks. This paper explains the procedure for building a binary probability tree from a given potential, which is similar to the one employed for building standard probability trees. It also offers a way of pruning a binary tree in order to reduce its size. This allows us to obtain exact or approximate results in inference depending on an input threshold. This paper also provides detailed algorithms for performing the basic operations on potentials (restriction, combination and marginalization) directly to binary trees. Finally, some experiments are described where binary trees are used with the variable elimination algorithm to compare the performance with that obtained for standard probability trees. (C) 2010 Elsevier Inc. All rights reserved.
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